| Title:
|
Seeking a network characterization of Corson compacta (English) |
| Author:
|
Feng, Ziqin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
513-521 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We say that a collection $\mathcal{A}$ of subsets of $X$ has property $(CC)$ if there is a set $D$ and point-countable collections $\mathcal{C}$ of closed subsets of $X$ such that for any $A\in \mathcal{A}$ there is a finite subcollection $\mathcal{F}$ of $\mathcal{C}$ such that $A=D\setminus \bigcup \mathcal{F}$. Then we prove that any compact space is Corson if and only if it has a point-$\sigma$-$(CC)$ base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in ``A Biased View of Topology as a Tool in Functional Analysis'' (2014) by B. Cascales and J. Orihuela and as in ``Network characterization of Gul'ko compact spaces and their relatives'' (2004) by F. Garcia, L. Oncina, J. Orihuela, which asked whether there is a network characterization of the class of Corson compacta. (English) |
| Keyword:
|
Corson compacta |
| Keyword:
|
point network |
| Keyword:
|
condition (F) |
| Keyword:
|
almost subbase |
| Keyword:
|
additively $\aleph_0$-Noetherian |
| MSC:
|
46B50 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 07511578 |
| idMR:
|
MR4405821 |
| DOI:
|
10.14712/1213-7243.2022.002 |
| . |
| Date available:
|
2022-02-21T13:33:44Z |
| Last updated:
|
2024-01-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149374 |
| . |
| Reference:
|
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